Workspace, joint space and singularities of a family of delta-like robot

• Published in: Mechanism and machine theory Vol. 127; pp. 73 - 95
• Main Authors: Jha, Ranjan, Chablat, Damien, Baron, Luc, Rouillier, Fabrice, Moroz, Guillaume
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2018; Elsevier
• Subjects: Computer Science; Cylindrical algebraic decomposition; Delta-like robot; Gröbner basis; Parallel robot; Robotics; Singularities; Workspace; Cylindrical algebraic decomposition; Gröbner basis; Singularities; Delta-like robot; Parallel robot; Workspace; Groebner basis
• ISSN: 0094-114X; 1873-3999
• DOI: 10.1016/j.mechmachtheory.2018.05.004

•Projection of parallel singularity curves in the joint space for the family of Delta-like robots.•Computation of serial singularities and 3-D plot of its projection in the workspace and joint space.•Complexity analysis for the serial singularities.•Analysis and 3-D plot of joint spaces. This paper presents the workspace, the joint space and the singularities of a family of delta-like parallel robots by using algebraic tools. The different functions of SIROPA library are introduced, which is used to induce an estimation about the complexity in representing the singularities in the workspace and the joint space. A Gröbner based elimination is used to compute the singularities of the manipulator and a Cylindrical Algebraic Decomposition algorithm is used to study the workspace and the joint space. From these algebraic objects, we propose some certified three-dimensional plotting describing the shape of workspace and of the joint space which will help the engineers or researchers to decide the most suited configuration of the manipulator they should use for a given task. Also, the different parameters associated with the complexity of the serial and parallel singularities are tabulated, which further enhance the selection of the different configuration of the manipulator by comparing the complexity of the singularity equations.